 # SQL Server pricing function for odd- first and last coupon bonds

OFL

Updated: 30 June 2014

Use OFL to calculate the price or yield of a bond with an odd first period, an odd last period, and a par value of 100. The OFL formula for a bond with an odd short first coupon is: Where

 A = C * accrued days / E C = 100 * coupon rate / frequency DFC = the number of days from the issue date to the first coupon date DLCi = the number of days from the previous coupon date to the lesser of the next coupon date and the maturity date in the ith last quasi-coupon period DSC = number of days from settlement to coupon E = the normal length of the first quasi-coupon period N = the number of coupons between the first coupon date and the last coupon date NCL = the number of quasi-coupons from the last coupon date to the quasi-maturity date NLLi = the normal length in days of the full ith quasi-coupon period in the odd last period RV = redemption value Y = yield / frequency

The OFL formula for a bond with an odd long first coupon is: Where

 Ai = number of accrued days for the ith quasi-coupon period C = 100 * coupon rate / frequency DFCi = number of days from the issue date to the first quasi-coupon date or the number of days in the quasi-coupon period
 DLCi = the number of days from the previous coupon date to the lesser of the next coupon date and the maturity date in the ith last quasi-coupon period DSC = number of days from settlement date to the next quasi-coupon date or first coupon date. E = number of days in the quasi-coupon period in which settlement occurs N = the number of coupons between the first coupon date and the maturity date NCF = number of quasi-coupon periods that fit in the odd first period NCL = the number of quasi-coupons from the last coupon date to the quasi-maturity date NLFi = normal length in days of the full ith quasi-coupon period within the odd period. NLLi = the normal length in days of the full ith quasi-coupon period in the odd last period Nqf = the number of whole quasi-coupon periods between the settlement date and the first coupon. RV = redemption value Y = yield / frequency

The OFL function allows you to pass value for DFC1, DFC2, A1, A2, NLF1, NLF2, DLC1, DLC2, NLL1, NLL2, NCL, NCF, N, Nqf, DSC, E, and RV directly into the equation and automatically calculates Y and C. OFL does not support bonds with more than 2 quasi-coupons in either the first or last coupon periods.
Syntax
SELECT [wctFinancial].[wct].[OFL](
<@Rate, float,>
,<@Yield, float,>
,<@Price, float,>
,<@RV, float,>
,<@Freq, int,>
,<@A1, float,>
,<@A2, float,>
,<@DSC, float,>
,<@E, float,>
,<@N, int,>
,<@ShortFirst, bit,>
,<@ShortLast, bit,>
,<@DLC1, float,>
,<@DLC2, float,>
,<@NLL1, float,>
,<@NLL2, float,>
,<@DFC1, float,>
,<@DFC2, float,>
,<@NLF1, float,>
,<@NLF2, float,>
,<@Nqf, int,>)
Arguments
@Rate
the bond's annual coupon rate. @Rate is an expression of type float or of a type that can be implicitly converted to float.
@Yield
the bond’s annual yield. @Yield is an expression of type float or of a type that can be implicitly converted to float.
@Price
the price of the bond. @Price is an expression of type float or of a type that can be implicitly converted to float.
@RV
the bond’s redemption value per 100 face value. @RV is an expression of type float or of a type that can be implicitly converted to float.
@Freq
the number of coupon payments per year. For annual payments, @Freq = 1; for semi-annual, @Freq = 2; for quarterly, @Freq = 4; for bimonthly @Freq = 6; for monthly @Freq = 12. @Freq is an expression of type float or of a type that can be implicitly converted to float.
@A1
the number of accrued days in the first quasi-coupon period of the odd first period. If @ShortFirst = 'True' or @ShortFirst = 'False' and @Nqf = 1 then this is the number of accrued days for the bond. If @ShortFirst = 'False' and @Nqf = 0 then this should be the same as the value entered in @DFC1. @A1 is an expression of type float or of a type that can be implicitly converted to float.
@A2
the number of accrued days in second quasi-coupon period in the odd first period. If @ShortFirst = 'True' then this should be NULL. @A2 is an expression of type float or of a type that can be implicitly converted to float.
@DSC
the days from settlement to next coupon date (when @N > 1) or the days from settlement to redemption (when @N = 1). @DSC is an expression of type float or of a type that can be implicitly converted to float.
@E
the number of days in the settlement period. @E is an expression of type float or of a type that can be implicitly converted to float.
@N
the number of coupons from the first coupon date to the last coupon date. @N is an expression of type int or of a type that can be implicitly converted to int.
@ShortFirst
a bit value which identifies the bond as having a short first coupon period ('True') or a long first coupon period ('False'). @ShortFirst is an expression of type bit or of a type that can be implicitly converted to bit.
@ShortLast
a bit value which identifies the bond as having a short last coupon period ('True') or a long last coupon period ('False'). @ShortLast is an expression of type bit or of a type that can be implicitly converted to bit.
@DLC1
the number of days from the last coupon date to the maturity date (when @ShortLast = 'True') or the number of days from the last coupon date to the quasi-coupon date (when @ShortLast = 'False'). @DLC1 is an expression of type float or of a type that can be implicitly converted to float.
@DLC2
the number of days from the quasi-coupon date to the maturity date. If @ShortLast = 'True' then @DLC2 should be NULL. @DLC2 is an expression of type float or of a type that can be implicitly converted to float.
@NLL1
the normal length of the first quasi-coupon period. @NLL1 is an expression of type float or of a type that can be implicitly converted to float.
@NLL2
the normal length of the second quasi-coupon period. If @ShortFirst = 'True' then @NLL2 should be NULL. @NLL2 is an expression of type float or of a type that can be implicitly converted to float.
@DFC1
the number of days from the issue date to the quasi-coupon date (when @ShortFirst = 'False') or the number of days from the issue date to the first coupon date (when @ShortFirst = 'True'). @DFC1 is an expression of type float or of a type that can be implicitly converted to float.
@DFC2
the number of days from in the second quasi-coupon period. If @ShortFirst = 'True' then @DFC2 should be NULL. @DFC2 is an expression of type float or of a type that can be implicitly converted to float.
@NLF1
the normal length of the first quasi-coupon period. @NLF1 is an expression of type float or of a type that can be implicitly converted to float.
@NLF2
the normal length of the second quasi-coupon period. If @ShortFirst = 'True' then @NLF2 should be NULL. @NLF2 is an expression of type float or of a type that can be implicitly converted to float.
@Nqf
the number of whole coupon periods between the settlement date and the first coupon date. If @ShortFirst = 'True' then @Nqf should be 0. @Nqf is an expression of type int or of a type that can be implicitly converted to int.
Return Type
float
Remarks
·         If @Rate is NULL then @Rate = 0.
·         If @RV is NULL then @RV = 100.
·         If @Freq is NULL then @Freq = 2.
·         If @E is NULL then @E = 180.
·         If @DSC is NULL then @DSC = 0.
·         If @N is NULL then @N = 0.
·         If @ShortFirst is NULL then @ShortFirst = 'True'.
·         If @ShortLast is NULL then @ShortFirst = 'True'.
·         If @A1 is NULL then @A1 = 0.
·         If @A2 is NULL then @A1 = 0.
·         If @DLC1 is NULL then @DLC1 = 0
·         If @DLC2 is NULL then @DLC2 = 0
·         If @DFC1 is NULL then @DFC1 = 0.
·         If @NLL1 is NULL then @NLL1 = 180.
·         If @NLL2 is NULL then @NLL2 = 180.
·         If @DFC1 is NULL then @DFC1 = 0.
·         If @DFC2 is NULL then @DFC2 = 0.
·         If @NLF1 is NULL then @NLF1 = 0.
·         If @NLF2 is NULL then @NLF2 = 0.
·         If @Nqf is NULL then @Nqf = 0.
·         If @Yield is NULL and @Price is NULL then NULL is returned.
·         If @E = 0 then NULL is returned.
·         If @Freq = 0 then NULL is returned.
·         C = 100 * @Rate/@Freq
·         Y = @Yield/@Freq
·         If @Yield is NOT NULL then price is calculated from the inputs otherwise yield is calculated from the inputs.
Examples
This is a bond with an odd short first period and odd short last period.
SELECT
wct.OFL(
.03125,  --@Rate
.02875,  --@Yield
NULL,    --@Price
100,     --@RV
2,       --@Frequency
87,      --@A1
NULL,    --@A2
11,      --@DSC
181,     --@E
18,      --@N
'True',  --@ShortFirst
'True',  --@ShortLast
44,      --@DLC1
NULL,    --@DLC2
184,     --@NLL1
NULL,    --@NLL2
98,      --@DFC1
NULL,    --@DFC2
NULL,    --@NLF1
NULL,    --@NLF2
0        --@Nqf
) as PRICE
This produces the following result.
PRICE
----------------------
102.00036224598
This is a bond with an odd long first coupon and an odd long last coupon.
SELECT
wct.OFL(
.03125,  --@Rate
.02875,  --@Yield
NULL,    --@Price
100,     --@RV
2,       --@Frequency
100,     --@A1
170,     --@A2
11,      --@DSC
181,     --@E
18,      --@N
'False', --@ShortFirst
'False', --@ShortLast
184,     --@DLC1
74,      --@DLC2
184,     --@NLL1
181,     --@NLL2
100,     --@DFC1
181,     --@DFC2
184,     --@NLF1
181,     --@NLF2
) as PRICE
This produces the following result.
PRICE
----------------------
102.103433425767
This is a bond with an odd long first coupon and an odd short last coupon.
SELECT
wct.OFL(
.03125,  --@Rate
NULL,    --@Yield
101.999004756314,    --@Price
100,     --@RV
2,       --@Frequency
100,     --@A1
170,     --@A2
11,      --@DSC
181,     --@E
18,      --@N
'False', --@ShortFirst
'True'--@ShortLast
44,      --@DLC1
NULL,    --@DLC2
184,     --@NLL1
NULL,    --@NLL2
100,     --@DFC1
181,     --@DFC2
184,     --@NLF1
181,     --@NLF2
) as YIELD
This produces the following result.
YIELD
----------------------
0.0287500000072949

This is a bond with an odd short first coupon and an odd long last coupon.
SELECT
wct.OFL(
.03125,     --@Rate
NULL,       --@Yield
102.104790915433,    --@Price
100,        --@RV
2,          --@Frequency
87,         --@A1
NULL,       --@A2
11,         --@DSC
181,        --@E
18,         --@N
'True',     --@ShortFirst
'False',    --@ShortLast
184,        --@DLC1
74,         --@DLC2
184,        --@NLL1
181,        --@NLL2
98,         --@DFC1
NULL,       --@DFC2
NULL,       --@NLF1
NULL,       --@NLF2
0           --@Nqf
) as YIELD

This produces the following result.
YIELD
----------------------
0.0287500000109004

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